Continuity conditions for finite-dimensional representations of some locally bounded groups

Necessary and sufficient conditions are obtained for the continuity of finite-dimensional representations of “almost divisible” locally pseudocompact groups in terms of the oscillations of these representations at a point. Applications to the continuity problem for finite-dimensional representations of almost connected locally compact groups and to the theory of quasirepresentations are given. To the blessed memory of Eckehart Hotzel Partially supported by the Russian Foundation for Basic Research under grant no. 02-01-00574, by the Program of Supporting the Leading Scientific Schools under grant no. NSh 619.203.1, and by an INTAS grant.